Power can be used to enter Keep Cards Draft (cost 50 power), Domain League (cost 50 power), or Battle Draft (cost 4 power).
There is currently no way to win more power.
You can trade Power or buy and sell it on the Market.
Unlike Gold, you can't buy Power with "real" money. It used to be something you gained if you were doing well in various Tournaments. For instance, you would get 4 Power if you won an Expert Clash, 2 if you were the runner up and 1 if you were third.